Author:
Bonnie Waltz, Deanna Mayers, Tracy Rains
Subject:
Mathematics, Algebra
Material Type:
Lesson Plan
Level:
High School
Grade:
9, 10, 11, 12
Tags:
  • Algebra
  • Graphing Infinite Solutions
  • Iowa Video
  • Iowa video
  • Linear Equations
  • Math
  • iowa-video
    License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    Downloadable docs, Interactive, Text/HTML, Video

    Education Standards

    Graphing Systems of Linear Equations

    Graphing Systems of Linear Equations

    Overview

    This seminar will allow you to solve a system of linear equations by graphing. It will help you to understand what it means when the lines in a system of equations are parallel, and also what it means for the graphs to be the same line. You will learn how to visually identify information about the system of equations simply by examining the graphs of the lines that make up the system.

    Standards

    CC.2.2.HS.D.10

    Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

    Engage

    Introductory warm-up activity.

    What do you think this graph represents?  What questions do you believe can be answered by looking at this graph?

     

    Capture.PNG

    Explore

    Read or watch the resources to learn about this concept, then do the practice activity.

    Read

    Watch

    Do

    The information in this link will show you how to solve a system of linear equations by graphing.  It will also show you examples of systems with special types of solutions. Be sure to work through all of the example problems that are included in the article.

    Watch the following video to learn how to solve a system of equations by graphing.  

    As you watch the video, complete the following graphic organizer.


     

    Click here in order to explore various graphs of systems of equations. Note: In the box marked “Round to”, select “Integer” from the drop-down menu.  Use this interactive tool in order to complete the graphic organizer found here.

    Explain

    Discuss your ideas / opinions / understandings.

    Answer the following questions using complete sentences.

    • What are the advantages to solving a system of equations using the graphing method?  What are the disadvantages?

    • Describe at least four pieces of information that may be obtained by looking at the graph of a system of equations.  

    Evaluate

    Now it is time to self-check how much you have learned about the this topic.  If you do not know as much as you thought, go back to the “Explore” section of this seminar and reread, rewatch, or redo the activities listed.  See your facilitator if you have questions.

    Click here to take the quiz online. You do not have to log into the quiz site in order to take this quiz. If a window pops up asking you to sign up for the quiz site, just close the sign-up window and start your quiz.

    Elaborate

    This is a task or project where you can show what you know.

    Directions:

    In the field of economics, the Law of Supply and Demand represents the crucial relationship between what consumers wish to buy and what suppliers are willing to sell. Research and define supply and demand, as well as the concept of market equilibrium. Be sure to clearly define each term on its own, and also discuss the relationships that exist among the three concepts.  

    Next, consider a market for chocolate bars. In this particular market, suppliers are only willing to produce 100 chocolate bars when the market price is $0.40 per bar, but will happily supply 500 bars at a market price of $2.00 per bar. Consumers will only demand 200 of the chocolate bars when the market price is $1.60 per bar, but demand will increase to 400 bars when the price is $0.80.     

    Write and graph equations to represent the supply and demand relationships that exist in this market for chocolate bars. When does this market achieve equilibrium? Explain your findings using mathematical calculations, a graph,  and complete sentences.

     

     

    Points Possible

    Points Earned

    Terms are clearly defined and relationships are clearly explained

    30

     

    Correct equations, graph, and equilibrium point

    30

     

    Clear, thorough explanation of findings

    30

     

    Total

    90

     

    Express

    Complete this wrap-up activity where you reflect on your learning.

    Many scenarios may be expressed as systems of linear equations. Once a system of equations is written, there are several options to choose from when solving.  Describe a scenario that may be expressed by a system of equations that you feel would best be solved by graphing the system.  Explain why you feel that graphing would be the best method to solve your system.